The present invention relates generally to nonlinear systems and more particularly to methods and systems for processing signals generated from nonlinear systems.
Virtually all practically engineered and/or natural systems experience nonlinear behavior. As defined herein, a nonlinear system is a system which exhibits a nonlinear relationship between its input and output (i.e., the system fails to obey the principal of superposition between its input and output). Examples of systems which exhibit nonlinear behavior include, inter alia, most biological systems, fluid flow systems, optical systems, imaging systems, RF receiver and transmitter systems, magnetic devices and magnetic recording systems, analog electronic systems, amplifier systems, loud speaker systems and radar systems.
A signal output from a nonlinear system typically includes a nonlinear component. As defined herein, use of the term signal in conjunction with nonlinear systems is meant to denote both (1) the mathematical description of any measurable phenomena in nature or in human-made systems and (2) the mathematically described function of one or more variable depending on one or more parameters. Examples of signals include, inter alia, light intensity, voltage, pressure, magnetic field strength and electric field strength.
Nonlinearities inherent in a particular system introduce nonlinear distortion products (e.g., harmonics, intermodulations, spurs, etc.) into the output signal generated by said system. In turn, the introduction of these nonlinear distortion products may limit the ability of signal processors to separate the desired component of the output signal (typically the linear component) therefrom, thereby effectively compromising the overall performance of the system, which is highly undesirable.
In particular, in the field of digital signal communications, nonlinear signal distortion is traditionally regarded as undesirable behavior which limits the performance of the overall system. As a result, nonlinear signal products are often treated in at least one of the following ways: (1) by reducing the nonlinear properties of selected devices within the system (often at a significant expense in cost) and/or (2) by minimizing the nonlinear distortion products present in the output signal using a nonlinear equalizer (NLEQ) digital signal processor at its back end (which often requires complex mathematical processes).
An example of one well-known type of NLEQ digital signal processor is disclosed in U.S. Pat. No. 6,639,537 to G. M. Raz (hereinafter the '537 patent), the disclosure of which is incorporated herein by reference. In the '537 patent, there is disclosed a highly linear analog-to-digital (ADC) conversion system that has an analog front-end device in cascade with a standard ADC converter, and a tunable digital nonlinear equalizer. The equalizer corrects the quantization distortion, deviations from ideal response, and additive noises generated by the analog front-end device and ADC converter.
Another example of a NLEQ digital signal processor is disclosed in a co-pending U.S. patent application entitled, “Method and System of Nonlinear Signal Processing” which was filed on even date herewith in the names of Gil M. Raz and Cy P. Chan (also referred to herein as simply “the Raz/Chan application”), the entirety of said disclosure being incorporated herein by reference.
One well-known system which typically experiences nonlinear irregularities is a receiver system (also referred to herein simply as a receiver). Referring now to FIG. 1, there is shown a simplified schematic representation of a receiver 11 which is well known in the art. Receiver 11 comprises an antenna 13 for receiving an analog signal s(n), an analog, low-noise, front end device 15 (e.g., a low-noise amplifier, mixer and/or filter) for conditioning (e.g., filtering and/or amplifying) analog signal s(n), and an analog-to-digital converter (ADC) 17 for converting the conditioned analog signal into a distorted, received digital output signal x(n). As can be appreciated, digital output signal x(n) includes certain nonlinear distortion products (e.g., harmonics, intermodulation products, etc.) which were created by front end device 15 and/or ADC 17.
Referring now to FIG. 2, there is shown a sample digital output signal x(n) generated in response to the injection of an analog input signal s(n) into nonlinear receiver system 11, said output signal x(n) being represented in terms of power as a function of frequency. As can be seen, the output signal x(n) includes a two tone signal (identified herein as the “target signal”) which represents the linear component (i.e., the desired component) of the digital output signal x(n). Under ideal conditions, the output signal x(n) generated by receiver system 11 would include only the target signal. However, imperfections inherent in the actual conditions tend to introduce a number of additional signal components in the output signal x(n), these additional signal components often compromising the usable portion of the target signal which can be used for processing and/or analysis (this usable portion of the target signal being used to define the dynamic range for the receiver).
Specifically, a plurality of factors typically influence the ability of receiver system 11 to accurately transform an incoming analog signal s(n) into a corresponding digital output signal x(n). Some of the factors which influence the overall performance of receiver 11 include, among other things:
(A) Noise—Noise is typically a broadband signal which is generated by various environmental effects (e.g., thermal noise) and/or man-made sources and is always present in physical environments. With respect to receiver 11, analog front end device 15 is typically responsible for the introduction of a considerable noise component into the output signal x(n). As can be seen in FIG. 2, the introduction of noise into the output signal (said noise component being identified simply as “noise” in FIG. 2) significantly reduces the usable portion of the target signal that can be used for processing, said usable portion being quantified typically by the signal-to-noise ratio (SNR). As a result, the signal-to-noise ratio is often utilized as one means for measuring the sensitivity of a receiver. Accordingly, in an effort to maximize the signal-to-noise ratio of a receiver (and thereby improve its sensitivity), receiver design engineers often utilize particular receiver components that produce low noise levels, often at a considerable expense in manufacturing costs for the overall system.
(B) Nonlinear Distortion Products—As described in detail above, systems which exhibit nonlinear behavior typically introduce nonlinear distortion products (e.g., harmonics, intermods, etc.) into their output signal. With respect to receiver 11, nonlinear distortion products are typically introduced into the output signal due to the nonlinear properties of analog front end device 15 and/or analog-to-digital converter 17. Additionally, the channel through which the signals arrive may have nonlinear characteristics as is the case with fiber optical communications systems. One type of nonlinear distortion product commonly produced by receiver systems is an intermodulation product, or intermod, (which is identified in FIG. 2 as “intermodulation products”). An intermodulation product is a form of a cross-modulation in which nonlinearities inherent in receiver 11 causes the target signal to appear to be modulated by an undesired signal (e.g., an interference signal). More generally, any spurious (spur) signal caused by the nonlinear system is a source of distortion to the desired signal and is characterized by the spur free dynamic range (SFDR). As can be seen in FIG. 2, the introduction of intermodulation products into the output signal x(n) significantly reduces the usable portion of the target signal that can be used for processing, said usable portion being quantified and identified simply as the intermodulation-free dynamic range (IFDR). Accordingly, in an effort to maximize the SFDR or IFDR of a receiver (and thereby improve its overall performance), receiver design engineers utilize various techniques for reducing nonlinear distortion products, some of said techniques being described in detail above.
(C) Interference Signals—An interference signal is an unwanted signal that often affects the ability of a system to isolate the desired component (i.e., the target signal) of a receiver's output signal. With respect to receiver 11, interference signals may either be natural or man-made, wherein man-made interference signals may be further characterized as either unintentional or intentional (e.g., a jammer signal). As can be appreciated, there are different well-known methods for treating (e.g., filtering) interference signals. For example, if an interference signal is well-defined in the frequency domain, digital signal processors often notch out the particular frequency band in which the interference signal lies. This process can be undesirable for numerous reasons including, inter alia, the circumstance when a portion of the target signal falls within the frequency range of the interference signal.
(D) Sampling rate—A sampling rate is defined as the rate at which an analog signal (a continuous-time signal) is sampled (e.g., in samples per second) in order to represent said analog signal in digital form. With respect to receiver 11, the sampling rate at which analog-to-digital converter 17 samples (i.e., digitizes in discrete time) the analog input signal s(n) as part of its signal conversion process can factor into the overall performance of receiver 11. Specifically, if the sampling rate chosen for ADC 17 is too high, the noise produced by receiver 11 often increases to an unacceptable level. Generally, the higher the sample rate in an ADC, the lower its commensurate SNR and SFDR. In addition, a high sampling rate typically increases the power requirement for receiver 11, thereby increasing costs. To the contrary, if the sampling rate chosen for ADC 17 is too low, aliasing may occur in the output signal x(n). Simply stated, aliasing relates to both: (1) the loss of some frequencies of the original signal when sampled at a slow rate and (2) the generation of frequency-shifted replicas of a target signal when the digitized signal is reconstructed as a continuous time signal. As will be shown in detail below, signal replicas caused from aliasing often create ambiguities and/or mixing with the target signal, which is highly undesirable.
Consequently, the sampling operation of an analog-to-digital converter is typically performed in accordance with the sampling theorem to ensure accurate representation and reconstruction of an analog signal in digital form. The sampling theorem states that, if the bandwidth of the received signal is f HZ, then at least two samples per cycle are needed for this component. In other words, the sampling rate must be at least 2f, said sampling rate being commonly referred to in the art as the Nyquist rate.
Use of the term affine in the context of the present invention refers to any addition of externals signals to the target signal, whether inadvertently (e.g., the presence of jammer signals) or by design using probe signals injected into the system by the system itself.
Nonlinear distortions are typically viewed as detrimental to system performance due to the creation of nonlinear distortion products (e.g., harmonics, intermods, spurs, etc.) which overlap the desired signals.
Interference signals caused by sources other than the target signal source are also typically considered to be detrimental to system performance. Strong interference signals are often referred to as jammers and clutter in the context of radar.